Select the the domain of the following fraction:
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Select the the domain of the following fraction:
The domain of a fraction depends on the denominator.
Since you cannot divide by zero, the denominator of a fraction cannot equal zero.
Therefore, for the fraction , the domain is "All numbers except 0," since the denominator cannot equal zero.
In other words, the domain is:
All numbers except 0
Determine if the simplification shown below is correct:
\( \frac{7}{7\cdot8}=8 \)
Division by zero is undefined in mathematics! Think of it this way: if 6 ÷ 0 had an answer, then that answer times 0 would equal 6. But any number times 0 equals 0, not 6.
Set the denominator equal to zero and solve! For , set x = 0. Since this is true when x = 0, exclude 0 from the domain.
That's totally fine! equals 0 (as long as x ≠ 0). The problem is only when the denominator is zero.
No! Never substitute excluded values. Instead, try a value that is in the domain, like x = 1: ✓
We write this as or using interval notation: (-∞, 0) ∪ (0, ∞). This means all real numbers except zero.
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